Like most (all?), when I started agility I didn't know about different venues. But the club I joined is a NADAC club. As far as I know, it was the only one in my area at the time, although there are/were others in other parts of the area, just not close (now there's multiple in this area). Anyhow, that's how I got started in NADAC.
I also was doing this with a mixed breed (a Malamute/Siberian) so AKC would've been out back then, anyhow.
My club IS a NADAC club, but we also have members that compete in the other venues, so while we focus on NADAC and hold NADAC shows, we also train for the other venues. I do enjoy having some variety now and then in class (teeter, tire, table... all of which were in NADAC when I started), but my heart is with NADAC.
I do NOT like AKC (although I'm glad they now allow mixes... and my club now has an AKC affiliation or whatever the proper terminology is... but I will not do AKC based on my own personal feelings). I've never done a USDAA trial. I don't have any ill feelings towards USDAA, but I just love NADAC so much more. I love the way the courses are. And with limited time and funds (not only do I do the dog thing, I work full time (which includes every other weekend), and I raise/train/show horses), I just stick to trialing in NADAC.
Can't say the other venues are different from personal experience (since I have none with them), but I LOVE the people in NADAC. Everyone is so friendly and helpful

I've also done a little ASCA. Way back when, our trials were dual sanctioned NADAC and ASCA. Now that doesn't happen. I like ASCA, but since they don't let my dog jump lower like NADAC does, I no longer do them. I personally don't feel my dog should have to jump higher than 16", so NADAC it is for us

(I have and compete multiple dogs, but that one is my main agility guy)